Spectral analysis of compass errors based on fast fourier transform and reduction absolute errors using a pass-band finite impulse response filter

Compass errors can be regarded as a deviation of the vessel from the expected heading. Gyrocompass errors are randomly oscillating in nature, and it is difficult to describe the behaviour of a gyrocompass sufficiently accurately using mathematical relationships. Fibre-optic gyroscopes have no mechanical components, so the variability in their indications has a different nature; the computational processes and inertial sensors used cause certain types of errors. Thus far, compass studies have focused on presenting absolute errors in the time domain. However, compasses exhibit specific characteristics in the frequency domain that affect the amplitude of their deviation. This leads to the issue of identifying the oscillatory spectrum of errors in the operation of such compasses, and how this spectrum is impacted by the dynamic movement of the vessel. We attempt to assess this phenomenon by means of measurements taken on board the training and research vessel M/S NAWIGATOR XXI. The application of a fast Fourier transform allows for calculation of the absolute compass errors in the frequency domain, meaning that the frequency of occurrence of errors can be observed as noise against the background of the useful signal. Our results confirm the value of applying a finite impulse response filter, which is used to filter out noise in the form of absolute compass errors from the useful signal background. The convolution function proposed here considerably extends the possibilities for analysing the signal spectrum in the frequency domain when testing for the accuracy of compass device indications, and enables the elimination of random errors with a low frequency of occurrence.

---

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki i promocja sportu (2025).